Safety and Reachability in Switched Nonlinear Systems Under Sampling and Quantization

In this work, we consider the problem of synthesizing controllers that robustly guarantee reachability to a given desired subset of the state space while satisfying a safety property defined in terms of state constraints. We allow for nonlinear dynamics with scalar inputs in each discrete mode, and possibly nonconvex state constraints. We make use of techniques from hybrid system verification to compute reachable sets, and then synthesize controllers that ensure safety and reachability properties under bounded model disturbances that vary continuously, as well as under effects of sampling and quantization. The resulting control policy is an explicit feedback law involving both a selection of continuous inputs and discrete switching commands at each time instant, based upon measurement of system state. The control inputs can be accessed in real time via a lookup table, and can be practically implemented in quantized sampled data systems. Simulation examples from aircraft conflict resolution and automated aerial refueling are used to illustrate applications of our approach.